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Molecular and electron-spin structures of a ring-shaped mixed-valence polyoxovanadate (IV, V) studied by 11B and 23Na solid-state NMR spectroscopy and DFT calculations
Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
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Molecular and electron-spin structures of a ring-shaped mixed-valence polyoxovanadate (IV, V) studied by 11B and 23Na solid-state NMR spectroscopy and DFT calculations Takahiro Iijima a,n, Toshihiro Yamase b,c, Katsuyuki Nishimura d a
Institute of Arts and Sciences, Yamagata University, Yamagata 990-8560, Japan Tokyo Institute of Technology, Nagatsuta, Yokohama 226-8503, Japan c MO Device Corporation, Kanazawa 920-0335, Japan d Institute for Molecular Science, Okazaki 444-8585, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 26 August 2015 Received in revised form 10 March 2016 Accepted 11 March 2016 Available online 14 March 2016
11
Keywords: POM Paramagnetic Antiferromagnetic Open shell Quadrupole MQMAS
B and 23Na solid-state nuclear magnetic resonance (NMR) spectra of ring-shaped paramagnetic crystals of H15[V7IVV5VB32O84Na4]·13H2O containing seven d1 electrons from VIV were studied. Magic-angle-spinning (MAS) and multiple-quantum MAS NMR experiments were performed at moderate (9.4 T) and ultrahigh magnetic fields (21.6 T). The NMR parameters for quadrupole and isotropic chemical shift interactions were estimated by simulation of the NMR spectra and from relativistic density functional theory (DFT) calculations. Four Na ions incorporated into the framework were found to occupy four distinct sites with different populations. The DFT calculation showed that d1 electrons with effectively one up-spin caused by strong antiferromagnetic interactions were delocalized over the 12 V ions. & 2016 Elsevier Inc. All rights reserved.
1. Introduction Polyoxometalates (POMs) are generally expressed as MxOyn (M ¼Mo, V, W, etc.). They are discrete early transition metal–oxide cluster anions with a size of 10 9–10 7 m [1–3]. In addition to their well-known catalytic behavior, their applications are expanding to electronic, optical, and medical devices and molecular nanocapsules owing to their unrivaled versatility and structural variation in both symmetry and size. In this work, the electronic structure of four Na þ -encapsulated ring-shaped polyoxovanadate (IV, V) of H15{Na4 ∈ [V12B32O84]}·13H2O (1) was investigated by 11B and 23Na solid-state NMR spectroscopy with quantum chemical calculations to understand the electronic interaction in mixedvalence POMs, which is very important in the research area of molecular devices. Solid-state nuclear magnetic resonance (NMR) spectroscopy is a well-known and efficient tool for analyzing local structures of solid materials. For half-integer quadrupole nuclei (HIQN) with I ¼3/2, 5/2, …, the central transition of |1/2〉 ↔ − |1/2〉 is affected by a second-order quadrupole interaction, and inhomogeneous n
Corresponding author. E-mail address: [email protected] (T. Iijima).
http://dx.doi.org/10.1016/j.ssnmr.2016.03.004 0926-2040/& 2016 Elsevier Inc. All rights reserved.
broadening of the spectra cannot be averaged completely using the conventional magic-angle-spinning (MAS) technique. The strength of the second-order quadrupole interaction of HIQNs can be reduced using a higher magnetic field [4]. In other, and combined, approaches, a multiple quantum (MQ) MAS method [5,6] has often been used to separate the chemical shift and quadrupole interactions, as well as satellite transition MAS [7,8], dynamic angle spinning [9,10], double rotation (DOR) [11,12], and MQDOR [13–15] methods. Structural studies of POMs or related materials by solid-state NMR have been performed using 31P MAS spectra [16–19], 31P spin-lattice relaxation time [20], 51V MAS spectra [21–23], 31P–51V rotational echo adiabatic passage double resonance [24], and 31 P–13C and 29Si–13C cross polarization [25]. Not only diamagnetic compounds but also paramagnetic solids [16–18,23] are the target materials. In particular, a paramagnetic solid with mixed-valence vanadium has been investigated by 51V NMR, electron spin resonance (ESR), and density functional theory (DFT) calculations to clarify the presence of the VIV and VV species [23]. Fig. 1 shows the structure of 1 ( ≡H15[V12B32O84Na4]·13H2O ) [26]. As shown in Fig. 1, five-coordinated V atoms form OVO4 square pyramids, formed by sharing edges cyclically to make a dodecavanadate ring ((VO)12O24). Nearly planar BO3 and distorted
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T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
VO5 BO3
BO4
V
O
B
Na
(a)
(b)
(i )
(i i )
Fig. 1. Structure of 1 expressed by (i) polyhedral and (ii) atom-and-bond models. (a) and (b) are the top- and side-view, respectively. (V atoms, VO5 square pyramids) and (B atoms, BO3 triangles, BO4 tetrahedra) are indicated by orange and green, respectively. In (ii), gray and yellow circles show O and Na atoms, respectively. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
tetrahedral BO4 units bridge each of the OVO4 pyramids. The overall doughnut-shaped structure, with approximate D4h symmetry, consists of the dodecavanadate ring sandwiched between hexadecaborate rings. Na ions are encapsulated in a large cavity of a [V12B32O84]19 ring with highly negative charges. The presence of eight Na sites with an occupancy of 0.5 results in a disordered structure. The four Na ions are considered to occupy positions related by an approximate Td symmetry (( x′, y′, z′), ( x′, −y′, −z′), ( −x′, y′, −z′) and ( −x′, −y′, z′)). Compared to B and V atoms in the framework, the Na ions have larger size of thermal ellipsoids [26]. From a simple calculation using the atomic coordinate and its standard deviation, the degree of fluctuation of the Na ions is estimated as 712.5 pm. The seven d1 electrons in 1 come from the mixed-valence [V7IVV5VB32O84]19 −. The spin state was estimated from magnetic measurements to be doublet at room temperature, because of strong antiferromagnetic exchange interactions [26]. The details of the structures of the encapsulated ions and electron spins, however, remain unclear. In the present paper, we report the 11B and 23Na (I¼ 3/2 in both cases) solid-state NMR spectra of 1. Because the crystal of 1, which contains d1 electrons, is paramagnetic and undergoes antiferromagnetic interactions, analysis of the NMR spectra is not straightforward [27–32]. The coupling constants of the quadrupole
and chemical shift interactions were therefore estimated from DFT calculations for the open-shell system [33–36]. The structure of the borate ring is known, therefore 11B MAS and MQMAS spectra were examined first to verify our analysis. 23Na NMR spectroscopy was performed under magnetic fields up to 21.6 T. Based on MAS and MQMAS results for the 23Na NMR spectra, the structure of the encapsulated Na ions was investigated. Finally, the electron-spin structure obtained from the DFT calculation was evaluated based on consistency with the solid-state NMR results.
2. Experimental Crystals of H15[V12B32O84Na4]·13H2O were synthesized using a previously reported method [26]. Samples for NMR spectroscopy were prepared by grinding to a fine powder in a mortar. 11 B and 23Na NMR spectra were obtained under a magnetic field (B0) of 9.4 T, using a Varian Inova 400 spectrometer, at resonance frequencies of 128.296 and 105.783 MHz, respectively. The 23Na NMR spectrum was also recorded at B0 ¼21.6 T, using a JEOL ECA 920 spectrometer, at 243.543 MHz. JEOL HX 4 mmϕ MAS probes for 400 and 920 NMR were used. The MAS frequency ( νr )
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
Table 1 Pulse parameters for the Parameter
11
B and
11
B (9.4 T)
17
23
Na 3QMAS NMR experiments for 1. 23
Na (9.4 T)
23
Na (21.6 T)
ν1exe /kHz
60
63
83
t exe/μs
9.0
5.2
3.8
ν1conv /kHz
60
63
83
t conv/μs
3.1
2.2
1.6
ν1soft/kHz
10
8
13
t soft/μs
15
15
10
tdw2/μs
5
5
5
tdw1/μs n2 n1 N
20
25
20
400 64 480
400 40 12,000
1024 128 1128
was 10–17 kHz. The frequency error was 750 Hz at the maximum. The 11B NMR spectra were referenced using 1M H3BO3 solution (19.6 ppm) as a secondary standard relative to BF3·Et2O [37,38]. The 23 Na NMR spectra were referred to the peak of 23Na in 1 M NaCl solution. One-dimensional MAS NMR spectra were obtained using a single 20° pulse. The radio frequency strength (ν1), dwell time ( tdw ), and number of scans for signal accumulation (N) were 60 kHz, 10 μs, and 4000, respectively, for 11B; 83 kHz, 5 μs, and 400, respectively, for 23Na at 9.4 T; and 13 kHz, 5 μs, and 800, respectively, for 23Na at 21.6 T. The 11B and 23Na 3QMAS spectra were obtained using a standard three-pulse sequence with a z-filter [39], where the coherence order passes from 0 → ± 3 → 0 → − 1. The pulse parameters were as follows: strengths and widths for the first 3Q excitation pulse ( ν1exc , t exc ), for the second conversion pulse (ν1conv , t conv ), and for the third soft detection pulse (ν1soft , t soft ), the dwell times in the direct and indirect dimensions ( tdw2 , tdw1), the number of acquisition points for the direct and indirect dimensions (n2, n1), and the number of accumulations for each t1 point (N). The used values are summarized in Table 1. The repetition delays were 0.05–0.3 s. Spectral simulation was performed using our own Fortran90 program, and considered the isotropic shift and second-order quadrupole interactions. For the electric field gradient (EFG) tensor, we defined the principal component as |eq33| ≥ |eq22| ≥ |eq11| and η = (eq11 − eq22) /eq33 as the asymmetry parameter. The parameter CQ = e2Qq33/h is the quadrupole coupling constant. A quarter-hemisphere was divided into ca. 13,000 points using a tiling scheme by Alderman et al. [40]. The time-domain NMR data were processed using our own program or the JEOL Delta software package. DFT calculations for the EFG and chemical shielding tensors were implemented using the Amsterdam Density Functional software package [41,42], version 2013.01 or 2014.04. The local Vosko–Wilk–Nusair density approximation augmented with the Becke–Perdew generalized gradient approximation was used as the exchange–correlation functional. Relativistic calculations with the zeroth-order regular approximation (ZORA) formalism [43–45], including scalar corrections, were performed for the open-shell system. The triple-ζ polarized Slater-type ZORA allelectron basis set was used. An isolated [V12B32(OH)8O76Na4]7 ion ({V12B32}) was used for the calculations. The X-ray structure of [V12B32O84Na4]15 [26] was slightly modified to a D2d symmetry, and eight protons were added to the eight terminal O atoms in the borate ring to obtain convergence of the self-consistent field (SCF) calculation. The positions of the H atoms were determined by geometry optimization with a non-relativistic DFT using the frozen-core double-ζ (DZ) basis set. Four Na atoms, related by an approximate Td symmetry, were set in the cavity of the polyoxovanadate. For the DFT calculations of the 23Na NMR
(a)
B3apex circ B3 B4
(b)
40
30
20
10 0 / ppm
-10 -20
Fig. 2. 11B MAS NMR spectra of 1 at B0 ¼9.4 T and νr = 17 kHz . (a) and (b) show the observed and simulated spectra, respectively. The red, blue and green dashed-lines in (b) show the spectral components of Bapex , Bcirc and B4, respectively. (For in3 3 terpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
parameters, structures with displaced Na atoms were also adopted (vide infra); the calculations were performed with the DZ allelectron basis set. As a secondary reference, the 11B chemical shift of an isolated H3BO3 was calculated with the same conditions as for {V12B32} and set at 19.6 ppm. For 23Na, a Na63Cl62 þ cluster was made to estimate the chemical shift of 23Na for solid NaCl. The 23 Na chemical shift of the central Na atom in the cluster was set at 7.2 ppm [46].
3. Results and discussion 3.1. Structure of borate ring by
11
B NMR
Fig. 2(a) shows the 11B MAS NMR spectrum of 1 at a magnetic field strength of 9.4 T. The spectrum, spanning about 20–30 ppm, revealed considerable structure, which implies that the lineshape is a superposition of components from multiple 11B sites, and each component is broadened by the second-order quadrupole interaction and/or by fast paramagnetic relaxation. There are three crystallographically inequivalent 11B sites for the symmetrized ions of {V12B32}, as shown in Fig. 3. The borate ring is formed by 16 B atoms bridged by O atoms. A quarter of the ring consists of B atoms in one three-coordinated ( Bcirc 3 ) and two four-coordinated (B4) units, to make a circle. Furthermore, the two BO4 units make a vertex-sharing, six-membered B3O6 structure with a triangular BO3 unit ( Bapex ). 3 A 11B 3QMAS experiment was conducted to obtain information on the spectral components of each 11B site. The obtained 3QMAS spectrum after shearing transformation [47] is shown in Fig. 4. For crystalline samples, the projection of the 3QMAS spectrum onto the indirect (F1) axis becomes a high-resolution spectrum, because inhomogeneous broadening caused by second-order quadrupole coupling is removed in this dimension. The F1 projection for 1 gave a resolved spectrum. The peaks at F1 ¼ 14.9 and 26.1 ppm are the spinning sidebands from a resonance at F1 ¼5.6 ppm. Note that
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T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
νr = 10 kHz corresponds to 20.6 ppm on the F1 axis, because of scaling by a factor of 9/34 in 3QMAS of I ¼3/2 nuclei [6]. Two distinct 11B sites are therefore present. 11 B NMR spectra for each 11B site can be retrieved by slicing the 11 B 3QMAS spectrum along the F2 axis at the resolved peak in the F1 axis. The two sliced spectra for 1 are shown on the right-hand
B (a)
O
B3circ
B3apex B4
(b)
B4 Fig. 3. Structure for one quarter of the hexadecaborate ring shown by (a) stick-andball model and (b) schematic representation. The green and gray circles show B and O atoms, respectively. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
side in Fig. 4. One more 11B component, which was observed in the 11 B MAS NMR spectrum but not detected in the 11B 3QMAS spectrum, is considered to be caused by its very small or very large quadrupole coupling. Spectral simulation was performed such that (i) the 11B MAS spectrum was fabricated from the sum of three 11B components with relative intensities of Bapex : Bcirc 3 : B4 = 1: 1: 2, 3 11 and (ii) two of the B components reproduce the slices of the 11B 3QMAS spectrum. The results of the spectral simulation, considering the secondorder quadrupole and isotropic shift interactions, are shown in Fig. 2(b) and the right-hand side of Fig. 4. The parameters of the quadrupole ( CQ , η) and isotropic shift (δ) interactions obtained by simulation are summarized in Table 2. For paramagnetic compounds, the isotropic component δ is the sum of the chemical shift ( δics) and the Fermi contact shift ( δFC ) due to the hyperfine coupling. However, δFC of 1 is expected to be small, because the spin densities of the unpaired electron spin at the 11B sites are very low [36] (vide infra). The NMR parameters were also obtained by DFT calculations, where δics is calculated as an isotropic value (Table 2). The analysis of the line broadening of the 11B NMR spectrum for the paramagnetic compound 1 is not straightforward. In the simulation, the broadening of each spectral component was adjusted simply by the effective spin–spin relaxation time ( T2⁎), and , Bcirc the values used for 11B of Bapex 3 , and B4 were 3.0 70.5, 3 1.0 70.2, and 0.5 70.04 ms, respectively. These values can be estimated, because the relative spectral intensity is also affected by T2⁎. The experimental value of the 11B spin–lattice relaxation time (T1) of 1 was 14 ms. The three 11B components were assigned as follows. (i) The components with large CQ values with relative spectral intensities of 1 and small CQ values with intensities of 2 are 11B of the BO3 and
Simulated component of the MAS spectrum
Observed -20
*
-10
F1 (ppm)
0
B3circ
10 20
*
30
B3apex
20
40 40
30
20 10 0 F2 (ppm)
10
0
υ / ppm
-10
20
10
0
υ / ppm
-10
-10 -20
Fig. 4. 11B 3QMAS NMR spectra of 1 at B0 ¼ 9.4 T and νr = 10 kHz . The asterisks in the map show the spinning sidebands. On the right-hand side, the slice spectra of 3QMAS at F1 ¼ 5.6 and 30.3 ppm are shown along with the theoretical spectra.
Table 2 NMR parameters of
11
B in {V12B32} obtained by spectral simulation and relativistic DFT calculation. η
δ/ppm
2.7 7 0.2
0.2 7 0.1
197 2
1.65 1.3 7 0.2
0.29 0.8 7 0.2
137 2
1.41 0.5 7 0.5 0.32
0.72 0.5 7 0.5 0.78
Site
Method
CQ /MHz
Bapex 3
By spectra By DFT By spectra By DFT By spectra By DFT
Bcirc 3 B4
δics/ppm
19 11 167 2 7
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
19
(a) Na(2)
Na(1)
Na(3)
Na(1) Na(2) Na(3)
Na(4)
(b)
Na*
50
0 υ / ppm (i)
Na(4) Na*
-50
40
20
0 -20 -40 υ / ppm (ii)
Fig. 5. 23Na MAS NMR spectra of 1 at (i) 9.4 and (ii) 21.6 T. (a) and (b) show the observed and simulated spectra, respectively. The red, blue, green, orange and black dashedlines in (b) show the spectral components by Na(1), Na(2), Na(3), Na(4) and Nan, respectively. The νr value was 16 kHz for both spectra. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
BO4 units, respectively. (ii) For the two types of BO3 unit, the sites and Bcirc with small and large η values correspond to Bapex 3 , re3 spectively. According to the previous studies for diamagnetic compounds [48,49], typical values for the 11B chemical shift are ∼20 ppm for BO3 and ∼0 ppm for BO4 units. Thus the present δics values for Bcirc and B4 are small and large, respectively, compared 3 to the literature values. Because the contribution of Fermi contact is not included in δics, these unusual δics values are considered to be due to the electronic structure of 1 adopting the open shell system and undergoing the antiferromagnetic coupling. The δ and δics values agreed well, except for B4. The disagreement in the B4 site may be caused by (I) the symmetry-imposed structure of {V12B32}, (II) other molecules (H2O and {V12B32}) surrounding the target {V12B32} molecule that were discarded in the DFT calculations, and (III) the Fermi contact shift. Although the η value for B4 could not be specified from the spectral simulation because of the small CQ value, the values of the other quadrupole parameters obtained by spectral simulation agreed with those obtained from DFT calculations, except in the . This disagreement can be caused by the reacase of CQ for Bapex 3 sons (I) and (II) above. The CQ value for Bcirc 3 seems somewhat small as a value for the BO3 unit. In the point-charge approximation (PCA), the component of the EFG tensor, eqαβ (α or β = x, y, z ), is expressed in SI units as [50,4]
eqαβ =
∑ j
qj
⎛ 3α β ⎞ ⎜ j j − δ ⎟, αjβj⎟ 2 rj ⎠
4π ϵ 0r j3 ⎜⎝
where the jth point-charge qj is at position
r 2j
=
x 2j
+
y2j
+
z 2j .
δαjβ and j
(1) (xj , yj , zj ) with
ϵ0 are the Kronecker delta and the free
space permittivity, respectively. By diagonalizing the EFG tensor of Eq. (1), the principal values are given. Considering the BO3 or BO4 unit and setting the charge for O2 as −2e , the eq33 values for Bapex , 3 21 21 Bcirc 3 , and B4 were calculated as 3.2 10 , 3.6 10 , and 20 2 circ 8.6 10 V m , respectively. The order eq33(B3 ) > eq33(Bapex ) 3
apex obtained by PCA is different from CQ (Bcirc ) by DFT cal3 ) < CQ (B3 culation and spectral simulation. This indicates that the small CQ (Bcirc 3 ) value is not simply caused by the local symmetry but the
charge distribution of 1. The sliced spectrum of 11B 3QMAS NMR at F1 ¼5.6 ppm was peak narrower than the simulated one. This is because the Bcirc 3 does not lie exactly along the F2 axis but is slightly inclined, because of the δ value distribution. In the MAS spectrum, this effect is taken into account by T2⁎. The poor signal-to-noise (SN) ratio of the observed sliced spectrum at F1 ¼ 30.3 ppm is the result of the large second-order quadrupole interaction for Bapex 3 ( CQ = 2.7 MHz ), causing spectral broadening and low conversion efficiency between single and triple quantum coherences. MQMAS spectra can also be analyzed by centers of gravity of the sliced spectra ( F2′ , F1′). If PQ = CQ 1 + η2/3 is defined as a second-order quadrupole effect, the values of δ (in units of parts per million) and PQ (in unit of hertz) can be estimated for the 3QMAS of I ¼3/2 nuclei as [6,51,52]
δ=
1 (17F1′ + 10F2′), 27
(2)
PQ =
ν 680 (F1′ − F2′) 03 , 27 10
where
ν0 is the resonance frequency. These equations give (δ, PQ )
(3)
and Bcirc as (25 ppm, 2.5 MHz) and (6 ppm, values for Bapex 3 3 0.9 MHz), respectively. There are some differences between the NMR parameters obtained by the analysis of the center of gravity and those by spectral simulation. This is due to the 11B 3QMAS spectrum that has the Bapex signal with low SN ratio and the 3 slightly inclined peak of Bcirc 3 . The 11B component that disappeared in the 3QMAS spectrum corresponds to B4. This is reasonable because both the spectral simulation and DFT calculation gave small CQ values, for which excitation to triple quantum coherence occurs inefficiently. Although the spectral lineshape of the 11B MAS NMR in Fig. 2 can be generated from CQ (for B4) up to 1.0 MHz, the value is considered to be very small. This small value is also expected from the BO4 structure, because the EFG of the nucleus at the center of the regular tetrahedral symmetry becomes zero by PCA. A slight distortion of BO4 from this symmetry causes the small CQ value in 1.
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T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
Table 3 23 Na NMR parameters of lativistic DFT calculation.
-40 (a)
QIS
F1 (ppm)
-20
CS
0
Na(1) Na(2)
20 Na(3) 40 40
F1 (ppm)
-10
20
0 -20 F2 (ppm)
-40
(b) Na(1)
0
Na(2)
10
Na(3) 20
CS 20
QIS 0 10 F2 (ppm)
-10
Fig. 6. 23Na 3QMAS NMR spectra of 1 at (a) 9.4 and (b) 21.6 T. The two solid lines indicated in the map show the axes of chemical shift (CS) and quadrupole-induced shift (QIS). The νr value was 16 kHz for both spectra.
For paramagnetic solids, in addition to the isotropic Fermi contact shift, the anisotropic interaction due to nuclear-electron dipole couplings ( /P ) can contribute to the spectra. The effect of /P on the 11B MAS spectra was examined in the Supporting Information (Figs. S1–S4). The spectral lineshape changed at slower MAS and larger anisotropy of /P . However, even at νr = 10 kHz , with only a slight change was found for the 11B MAS spectra of Bcirc 3 the anisotropy estimated for this site. Therefore, at least the contribution from the /P term in the spectral simulation in Fig. 2 (b) can be safely neglected. Experimentally, very intense spinning sidebands, which are a feature of the strong /P interaction, were not observed. 3.2. Structure of encapsulated Na ions by
23
Na NMR
Fig. 5(a-i) and (a-ii) show the 23Na MAS NMR spectra of 1 at 9.4 and 21.6 T, respectively. The broadened spectrum at 9.4 T
23
Na in {V12B32} obtained by spectral simulation and re-
Site
CQ /MHz
η
δ/ppm
〈By Spectra〉 Na(1) Na(2) Na(3) Na(4)
1.8 7 0.4 0.6 7 0.6 0.9 7 0.9 0.5 7 0.5
0.5 7 0.5 0.5 7 0.5 0.5 7 0.5 0.5 7 0.5
574 172 15 7 4 673
〈By DFT〉 Na
3.80
0.2
δics/ppm
26
narrowed at 21.6 T, as a result of the increase in the isotropic chemical shift (in hertz) and the decrease in the second-order quadrupole coupling when the high-field magnet is used (the chemical shift dispersion is not so large for this sample, as shown below). These spectra imply that there are at least two Na sites in 1. In order to improve the resolution, 23Na 3QMAS NMR spectra were obtained. The 3QMAS spectra obtained at 9.4 and 21.6 T are shown in Fig. 6(a) and (b), respectively. Clearly, three distinct 23Na sites are present in 1 (Na(1) to Na(3), from lower to higher frequency). For amorphous compounds, two lines, called the chemical shift (CS) axis and the quadrupole-induced shift (QIS) axis, are drawn in the MQMAS spectra [51,52]. The contours of the peaks in the 23Na 3QMAS spectra of Fig. 6 tend to lie along the CS axis, indicating a distribution of the chemical shift. The 23Na 3QMAS spectra can also be analyzed using Eqs. (2) and (3). With the maximum peak position of the 23Na 3QMAS spectra ( F2′ , F1′), the values of (δ, PQ ) for Na(1), Na(2), and Na(3) were estimated as ( 1 ppm, 1.6 MHz), (5 ppm, 0.8 MHz), and (18 ppm, 0.8 MHz), respectively, from the 23 Na 3QMAS at 9.4 T, and ( 7 ppm, 1.7 MHz), (0 ppm, 0.8 MHz), and (13 ppm, 0.8 MHz), respectively, at 21.6 T. The three 23Na sites were used to simulate the 23Na MAS spectra. The observed spectra, however, could not be reproduced by the superposition of these three sites alone. For example, a sharp peak at 12 ppm and a broad component extending across 20 to 40 ppm in Fig. 5(a-ii) are not generated by Na(1)–Na(3). The 23Na sites corresponding to these peaks are required to have very large or very small CQ values, because they were not observed in the 23Na 3QMAS spectra. By simulating the spectra at two magnetic fields, two separate 23Na sites (Na(4) and Nan) with very small CQ value were needed. The simulation results are shown in Fig. 5(b-i) and (b-ii). The NMR parameters for the sites Na(1)–Na (4) obtained by the simulation of the MAS spectra are summarized in Table 3. The line width of each spectral component was again adjusted by T2⁎, and the values were 0.3 7 0.1 ms for Na(1)–Na (3) and 0.55 70.1 ms for Na(4). The experimental 23Na T1 value of 1 was 2.7 ms. Setting the spectral intensity for Na(1) at 1.0, the relative intensities for Na(2), Na(3), and Na(4) were 0.19 70.11, 0.327 0.04, and 0.09 70.05, respectively. It is noted that because the low-frequency peak is very broad, the peak for the Na* site was produced by a Gaussian distribution. The peak center and standard deviation for the Gaussian were 29 73 and 6 7 1 ppm, respectively. The effect of the hyperfine interaction on the 23Na spectra was neglected as in the case of the 11B spectra. The isotropic component is not expected, because the electron spin density is almost localized on the V sites, and there are four bonds between the V and Na atoms. Furthermore, for the anisotropic component, the dipole interaction of 23Na–VIV is smaller than that of 11B–VIV because of the longer internuclear distance and small gyromagnetic ratio. From the simulation analysis for the paramagnetic effect (Figs. S5–S7), it is found that we can ignore the paramagnetic
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
contribution to the 23Na spectra of 1. Because of the fast spin relaxation, each spectral component was broadened and the η value could not be estimated. Considering that 1 + η2/3 can vary from 1.00 to 1.15, the quadrupole parameters obtained by spectral simulation are consistent with the PQ values obtained from the 23Na 3QMAS spectra. Although CQ for Na(4) was estimated as 0.5 7 0.5 MHz from the spectral simulation in Fig. 5, the value would be very small because the signal was not observed in the 23Na 3QMAS spectra. The CQ range for Na(2) is similar to that for Na(4) in Table 3. Thus, the Na (2) component, which exhibits the 23Na 3QMAS peak, is expected to have relatively large CQ value in the range. According to literature, the 23Na chemical shifts at room temperature have been reported as 5.3 to 8.8 ppm, 1.4 to 18.3 ppm [53], and 1.5 to 18.0 ppm, 1.2 to 14.4 ppm [54] for Na ions at cation sites within zeolites, and 20.5–2.4 ppm [55] for those within the zeolite-like Ge-framework. Thus, the estimated δ values for Na(1)–Na(4), collectively extending over 19 to 9 ppm, seem reasonable. Single-crystal X-ray data at room temperature [26] show that the four Na ions incorporated into the ring-shaped framework are located at the corners of a slightly distorted rectangular-parallelepiped with edge lengths of 267–273 and 285–287 pm. The multiple Na sites observed in the 23Na NMR spectra are therefore not so surprising. The Nan site may be due to the impurity incorporated in 1, because the δ value extends centered at 2973 ppm. A DFT calculation provided only a set of NMR parameters (Table 3), because the four Na ions are crystallographically equivalent in the simplified model considered in the calculations with D2d symmetry. A suitable method for examining the differences in the chemical shifts among the sites by DFT calculations is to use the X-ray structure or to perform geometry optimization for the Na ions. Unfortunately, the SCF calculations could not be converged without imposing symmetry. We therefore displaced the Na ions manually in a structure having an overall D2 symmetry. The calculation results for the Na-position dependence of the δics value of 23Na NMR are shown in Fig. 7. The coordinates are defined such that the four Na ions are located at ( x′, y′ , z′), ( x′, − y′ , − z′), ( −x′, y′ , − z′), and ( −x′, − y′ , z′). The values of Δx, Δy , and Δz are the displacements from the Na position in the original D2d structure. A negative displacement means that the Na ions approach the center of the cavity. At each Δz value, the δics values were calculated with the Δx and Δy values changing from 40 to 40 pm in steps of 20 pm. Basically, the maps in Fig. 7 are the upslope toward the lower left, and the gradient increases with decreasing Δz . The δics value at ( Δx, Δy , Δz )¼( 20 pm, 40 pm, 20 pm) was 4 ppm, which differs from the value at (0 pm, 0 pm, 0 pm) by 28 ppm. Therefore, the large difference of the δ values between the Na(1)–Na(4) sites can be understood. Because the simplified molecular structure was used in the DFT calculation, the absolute shift values obtained from the spectra and the DFT calculations differ, and large displacement of the Na position was required for explaining the observed 23Na shift. The relative spectral intensities (Fig. 5) indicate that the four Na ions occupy distinct sites with different populations. A similar phenomenon has been reported for the Na ions within the NaY zeolite [53]; three 23Na sites with different population were observed by NMR, contrary to a result from the molecular simulation predicting that the Na ions would be at a single site. The multiple sites were caused by a potential surface of the Na ion with multiple local minima. If the relative intensities of the 23Na peak of 1 are related to the potential surface in the cavity, the depth of the local minimum is in the order of Na(1) > Na(3) > Na(2) > Na(4). Thr bond energy of 1 was examined by the DFT calculation as a function of the displacement of the Na ion in the cavity (Fig. S8). Unlike the δics map in Fig. 7, the upslope of the contour toward the
21
40 (a) 20 Δy / pm 0 -20 -40 -40
-20
0 20 Δx / pm
40 δics / ppm 5 0
40 (b) 20
-5 -10
Δy / pm 0
-15 -20
-20
-25 -40 -40
-20
0 20 x / pm Δ
40
-20
0 20 Δx / pm
40
-30
40 (c) 20 Δy / pm 0 -20 -40 -40
Fig. 7. Contour maps for δics of 23Na NMR of {V12B32} obtained by relativistic DFT calculation and plotted as a function of Δx and Δy . (a), (b) and (c) show the plots at Δz = 0 , 10 and 20 pm, respectively. See text for the meaning of Δx, Δy and Δz .
lower left of the map was not simple for the bond energy, which may be due to the multiple local minima of the potential surface. Neither the accurate positions of the Na ions nor the type of disorder could be determined in the present analysis. The CQ values obtained by spectral simulation are smaller than those obtained from DFT calculations (Table 3). This can be ascribed to a slight change in the local symmetry of the Na sites. A partial averaging of the EFG tensor caused by fluctuation of the Na ions in the cavity may also reduce the CQ value. 3.3. Electron spin structure Seven d1 electrons are included in the [V7IVV5VB32O84]19 − anion.
22
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
(a)
(b)
cancelation of the up- and down-spins in the units, one up-spin is the total density for {V12B32}. The occupancy by VIV species is reduced to 7/12 for each V ion on average. It is noted that although the electronic structure can be altered by the position of the Na ions, no drastic position-dependence was obtained for the spin density distribution (Fig. S9). Because the spin density exhibits narrow spread on each V site, the Fermi contact interactions in the 11 B and 23Na NMR spectra are expected to be reduced considerably. Although we attempted to record 51V MAS NMR spectra of 1, no signal was observed. This result is consistent with the delocalized spin structure obtained from the DFT calculation, because the relaxation time of 51V is expected to be considerably short owing to the electron spins being distributed on all the V sites. If the electron spin is localized on a 51V site, the 51V NMR signals would be observed for other 51V sites [23], if the structural disorder of the framework is static. An X-band ESR signal at 7.2 K for the crystalline form of 1 was a singlet-like broadened spectrum without hyperfine structures (g ¼2.0 with peak-to-peak halfwidth, ΔHpp , of 47 mT) (Fig. S10). When VIV is delocalized over the 12 V sites, the spectrum consists of 85 lines caused by 2In þ1(I ¼7/2, n ¼12). Considering signal overlaps due to anisotropic interactions, the singlet-like broadened spectrum due mainly to intense peaks arising from Ieff = ± 3/2 and 71/2 is expected. Indeed, such an ESR spectrum ( ΔHpp ∼ 40 mT ) has been reported for a typical spin-frustration compound of K11H[(VO )3(SbW9O33)2]·27H2O [56], where effectively one d1 electron is delocalized over a VIV 3 ring, whereas the two other electrons are antiferromagnetically coupled. If the d1 electron is localized on a site, a narrower spectrum with eight lines will appear. Therefore, the above delocalized spin structure of 1 is also supported by the ESR spectrum.
4. Conclusion Fig. 8. Spin density distribution of {V12B32} obtained by relativistic DFT calculation. (a) and (b) show the top- and side-view, respectively. The distributions for the upand down-spins are indicated by blue and red, respectively. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Only one uncoupled electron is effective at room temperature, because of strong antiferromagnetic couplings, therefore the difference between the up- and down-spins was set at one in the DFT calculation. Here, we consider two types of molecular and electron spin structures [26]. One has structural disorder in the {V12B32} framework, where three sets of antiferromagnetic couplings occur as a result of the disorder of the V atoms (or the OVO4 pyramids), leaving one electron spin localized on a V IV site. The other is an average structure with electron spins delocalized over the ring. For the DFT calculation of the former structure, the symmetry of {V12B32} needs to be released, because three V–V pairs with short interatomic lengths are required for the framework structure. The SCF calculations for such structures, however, have never converged, as in the case for 23Na NMR. We therefore calculated the spin structure for the original D2d structure again, which is the average structure. The spin density distribution of the d1 electrons in {V12B32} obtained from the DFT calculation is shown in Fig. 8. Because of the symmetry, the electron spins were delocalized over the 12 V ions. A spin density unit consists of a down-spin with two up-spins on both sides, caused by antiferromagnetic interactions. This corresponds to a molecular structure with V–V interatomic distances of 289.4 pm for the V ions in the V–V–V unit, and 303.6 pm for those between the units. Because of partial
In conclusion, we studied the 11B and 23Na MAS and 3QMAS solid-state NMR spectra at 9.4 and 21.6 T for the mixed-valence paramagnetic polyoxovanadate(IV, V) of 1. The NMR parameters were estimated using spectral analysis and relativistic DFT calculations. The four Na ions incorporated into the ring-shaped framework occupied the four sites in the cavity, with different populations. The seven d1 electrons from VIV species were distributed over the 12 V ions, resulting in an average VIV occupancy of 7/12 for each of them. Future work will include (i) variable-temperature 11 B static NMR to observe the spectral change through the magnetic interaction and (ii) variable-temperature 23Na NMR and molecular dynamics simulation to investigate the motion of the Na ions in the cavity.
Acknowledgment This work was supported by the IMS molecule and material synthesis platform as a program of “Nanotechnology Platform” of MEXT, Japan. The financial support by JSPS Grant-in-Aid for Young Scientists (B) No. 24750026 is gratefully acknowledged.
Appendix A. Supplementary data Supplementary data associated with this paper can be found in the online version at http://dx.doi.org/10.1016/j.ssnmr.2016.03.004.
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
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Contents lists available at ScienceDirect
Solid State Nuclear Magnetic Resonance journal homepage: www.elsevier.com/locate/ssnmr
Molecular and electron-spin structures of a ring-shaped mixed-valence polyoxovanadate (IV, V) studied by 11B and 23Na solid-state NMR spectroscopy and DFT calculations Takahiro Iijima a,n, Toshihiro Yamase b,c, Katsuyuki Nishimura d a
Institute of Arts and Sciences, Yamagata University, Yamagata 990-8560, Japan Tokyo Institute of Technology, Nagatsuta, Yokohama 226-8503, Japan c MO Device Corporation, Kanazawa 920-0335, Japan d Institute for Molecular Science, Okazaki 444-8585, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 26 August 2015 Received in revised form 10 March 2016 Accepted 11 March 2016 Available online 14 March 2016
11
Keywords: POM Paramagnetic Antiferromagnetic Open shell Quadrupole MQMAS
B and 23Na solid-state nuclear magnetic resonance (NMR) spectra of ring-shaped paramagnetic crystals of H15[V7IVV5VB32O84Na4]·13H2O containing seven d1 electrons from VIV were studied. Magic-angle-spinning (MAS) and multiple-quantum MAS NMR experiments were performed at moderate (9.4 T) and ultrahigh magnetic fields (21.6 T). The NMR parameters for quadrupole and isotropic chemical shift interactions were estimated by simulation of the NMR spectra and from relativistic density functional theory (DFT) calculations. Four Na ions incorporated into the framework were found to occupy four distinct sites with different populations. The DFT calculation showed that d1 electrons with effectively one up-spin caused by strong antiferromagnetic interactions were delocalized over the 12 V ions. & 2016 Elsevier Inc. All rights reserved.
1. Introduction Polyoxometalates (POMs) are generally expressed as MxOyn (M ¼Mo, V, W, etc.). They are discrete early transition metal–oxide cluster anions with a size of 10 9–10 7 m [1–3]. In addition to their well-known catalytic behavior, their applications are expanding to electronic, optical, and medical devices and molecular nanocapsules owing to their unrivaled versatility and structural variation in both symmetry and size. In this work, the electronic structure of four Na þ -encapsulated ring-shaped polyoxovanadate (IV, V) of H15{Na4 ∈ [V12B32O84]}·13H2O (1) was investigated by 11B and 23Na solid-state NMR spectroscopy with quantum chemical calculations to understand the electronic interaction in mixedvalence POMs, which is very important in the research area of molecular devices. Solid-state nuclear magnetic resonance (NMR) spectroscopy is a well-known and efficient tool for analyzing local structures of solid materials. For half-integer quadrupole nuclei (HIQN) with I ¼3/2, 5/2, …, the central transition of |1/2〉 ↔ − |1/2〉 is affected by a second-order quadrupole interaction, and inhomogeneous n
Corresponding author. E-mail address: [email protected] (T. Iijima).
http://dx.doi.org/10.1016/j.ssnmr.2016.03.004 0926-2040/& 2016 Elsevier Inc. All rights reserved.
broadening of the spectra cannot be averaged completely using the conventional magic-angle-spinning (MAS) technique. The strength of the second-order quadrupole interaction of HIQNs can be reduced using a higher magnetic field [4]. In other, and combined, approaches, a multiple quantum (MQ) MAS method [5,6] has often been used to separate the chemical shift and quadrupole interactions, as well as satellite transition MAS [7,8], dynamic angle spinning [9,10], double rotation (DOR) [11,12], and MQDOR [13–15] methods. Structural studies of POMs or related materials by solid-state NMR have been performed using 31P MAS spectra [16–19], 31P spin-lattice relaxation time [20], 51V MAS spectra [21–23], 31P–51V rotational echo adiabatic passage double resonance [24], and 31 P–13C and 29Si–13C cross polarization [25]. Not only diamagnetic compounds but also paramagnetic solids [16–18,23] are the target materials. In particular, a paramagnetic solid with mixed-valence vanadium has been investigated by 51V NMR, electron spin resonance (ESR), and density functional theory (DFT) calculations to clarify the presence of the VIV and VV species [23]. Fig. 1 shows the structure of 1 ( ≡H15[V12B32O84Na4]·13H2O ) [26]. As shown in Fig. 1, five-coordinated V atoms form OVO4 square pyramids, formed by sharing edges cyclically to make a dodecavanadate ring ((VO)12O24). Nearly planar BO3 and distorted
16
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
VO5 BO3
BO4
V
O
B
Na
(a)
(b)
(i )
(i i )
Fig. 1. Structure of 1 expressed by (i) polyhedral and (ii) atom-and-bond models. (a) and (b) are the top- and side-view, respectively. (V atoms, VO5 square pyramids) and (B atoms, BO3 triangles, BO4 tetrahedra) are indicated by orange and green, respectively. In (ii), gray and yellow circles show O and Na atoms, respectively. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
tetrahedral BO4 units bridge each of the OVO4 pyramids. The overall doughnut-shaped structure, with approximate D4h symmetry, consists of the dodecavanadate ring sandwiched between hexadecaborate rings. Na ions are encapsulated in a large cavity of a [V12B32O84]19 ring with highly negative charges. The presence of eight Na sites with an occupancy of 0.5 results in a disordered structure. The four Na ions are considered to occupy positions related by an approximate Td symmetry (( x′, y′, z′), ( x′, −y′, −z′), ( −x′, y′, −z′) and ( −x′, −y′, z′)). Compared to B and V atoms in the framework, the Na ions have larger size of thermal ellipsoids [26]. From a simple calculation using the atomic coordinate and its standard deviation, the degree of fluctuation of the Na ions is estimated as 712.5 pm. The seven d1 electrons in 1 come from the mixed-valence [V7IVV5VB32O84]19 −. The spin state was estimated from magnetic measurements to be doublet at room temperature, because of strong antiferromagnetic exchange interactions [26]. The details of the structures of the encapsulated ions and electron spins, however, remain unclear. In the present paper, we report the 11B and 23Na (I¼ 3/2 in both cases) solid-state NMR spectra of 1. Because the crystal of 1, which contains d1 electrons, is paramagnetic and undergoes antiferromagnetic interactions, analysis of the NMR spectra is not straightforward [27–32]. The coupling constants of the quadrupole
and chemical shift interactions were therefore estimated from DFT calculations for the open-shell system [33–36]. The structure of the borate ring is known, therefore 11B MAS and MQMAS spectra were examined first to verify our analysis. 23Na NMR spectroscopy was performed under magnetic fields up to 21.6 T. Based on MAS and MQMAS results for the 23Na NMR spectra, the structure of the encapsulated Na ions was investigated. Finally, the electron-spin structure obtained from the DFT calculation was evaluated based on consistency with the solid-state NMR results.
2. Experimental Crystals of H15[V12B32O84Na4]·13H2O were synthesized using a previously reported method [26]. Samples for NMR spectroscopy were prepared by grinding to a fine powder in a mortar. 11 B and 23Na NMR spectra were obtained under a magnetic field (B0) of 9.4 T, using a Varian Inova 400 spectrometer, at resonance frequencies of 128.296 and 105.783 MHz, respectively. The 23Na NMR spectrum was also recorded at B0 ¼21.6 T, using a JEOL ECA 920 spectrometer, at 243.543 MHz. JEOL HX 4 mmϕ MAS probes for 400 and 920 NMR were used. The MAS frequency ( νr )
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
Table 1 Pulse parameters for the Parameter
11
B and
11
B (9.4 T)
17
23
Na 3QMAS NMR experiments for 1. 23
Na (9.4 T)
23
Na (21.6 T)
ν1exe /kHz
60
63
83
t exe/μs
9.0
5.2
3.8
ν1conv /kHz
60
63
83
t conv/μs
3.1
2.2
1.6
ν1soft/kHz
10
8
13
t soft/μs
15
15
10
tdw2/μs
5
5
5
tdw1/μs n2 n1 N
20
25
20
400 64 480
400 40 12,000
1024 128 1128
was 10–17 kHz. The frequency error was 750 Hz at the maximum. The 11B NMR spectra were referenced using 1M H3BO3 solution (19.6 ppm) as a secondary standard relative to BF3·Et2O [37,38]. The 23 Na NMR spectra were referred to the peak of 23Na in 1 M NaCl solution. One-dimensional MAS NMR spectra were obtained using a single 20° pulse. The radio frequency strength (ν1), dwell time ( tdw ), and number of scans for signal accumulation (N) were 60 kHz, 10 μs, and 4000, respectively, for 11B; 83 kHz, 5 μs, and 400, respectively, for 23Na at 9.4 T; and 13 kHz, 5 μs, and 800, respectively, for 23Na at 21.6 T. The 11B and 23Na 3QMAS spectra were obtained using a standard three-pulse sequence with a z-filter [39], where the coherence order passes from 0 → ± 3 → 0 → − 1. The pulse parameters were as follows: strengths and widths for the first 3Q excitation pulse ( ν1exc , t exc ), for the second conversion pulse (ν1conv , t conv ), and for the third soft detection pulse (ν1soft , t soft ), the dwell times in the direct and indirect dimensions ( tdw2 , tdw1), the number of acquisition points for the direct and indirect dimensions (n2, n1), and the number of accumulations for each t1 point (N). The used values are summarized in Table 1. The repetition delays were 0.05–0.3 s. Spectral simulation was performed using our own Fortran90 program, and considered the isotropic shift and second-order quadrupole interactions. For the electric field gradient (EFG) tensor, we defined the principal component as |eq33| ≥ |eq22| ≥ |eq11| and η = (eq11 − eq22) /eq33 as the asymmetry parameter. The parameter CQ = e2Qq33/h is the quadrupole coupling constant. A quarter-hemisphere was divided into ca. 13,000 points using a tiling scheme by Alderman et al. [40]. The time-domain NMR data were processed using our own program or the JEOL Delta software package. DFT calculations for the EFG and chemical shielding tensors were implemented using the Amsterdam Density Functional software package [41,42], version 2013.01 or 2014.04. The local Vosko–Wilk–Nusair density approximation augmented with the Becke–Perdew generalized gradient approximation was used as the exchange–correlation functional. Relativistic calculations with the zeroth-order regular approximation (ZORA) formalism [43–45], including scalar corrections, were performed for the open-shell system. The triple-ζ polarized Slater-type ZORA allelectron basis set was used. An isolated [V12B32(OH)8O76Na4]7 ion ({V12B32}) was used for the calculations. The X-ray structure of [V12B32O84Na4]15 [26] was slightly modified to a D2d symmetry, and eight protons were added to the eight terminal O atoms in the borate ring to obtain convergence of the self-consistent field (SCF) calculation. The positions of the H atoms were determined by geometry optimization with a non-relativistic DFT using the frozen-core double-ζ (DZ) basis set. Four Na atoms, related by an approximate Td symmetry, were set in the cavity of the polyoxovanadate. For the DFT calculations of the 23Na NMR
(a)
B3apex circ B3 B4
(b)
40
30
20
10 0 / ppm
-10 -20
Fig. 2. 11B MAS NMR spectra of 1 at B0 ¼9.4 T and νr = 17 kHz . (a) and (b) show the observed and simulated spectra, respectively. The red, blue and green dashed-lines in (b) show the spectral components of Bapex , Bcirc and B4, respectively. (For in3 3 terpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
parameters, structures with displaced Na atoms were also adopted (vide infra); the calculations were performed with the DZ allelectron basis set. As a secondary reference, the 11B chemical shift of an isolated H3BO3 was calculated with the same conditions as for {V12B32} and set at 19.6 ppm. For 23Na, a Na63Cl62 þ cluster was made to estimate the chemical shift of 23Na for solid NaCl. The 23 Na chemical shift of the central Na atom in the cluster was set at 7.2 ppm [46].
3. Results and discussion 3.1. Structure of borate ring by
11
B NMR
Fig. 2(a) shows the 11B MAS NMR spectrum of 1 at a magnetic field strength of 9.4 T. The spectrum, spanning about 20–30 ppm, revealed considerable structure, which implies that the lineshape is a superposition of components from multiple 11B sites, and each component is broadened by the second-order quadrupole interaction and/or by fast paramagnetic relaxation. There are three crystallographically inequivalent 11B sites for the symmetrized ions of {V12B32}, as shown in Fig. 3. The borate ring is formed by 16 B atoms bridged by O atoms. A quarter of the ring consists of B atoms in one three-coordinated ( Bcirc 3 ) and two four-coordinated (B4) units, to make a circle. Furthermore, the two BO4 units make a vertex-sharing, six-membered B3O6 structure with a triangular BO3 unit ( Bapex ). 3 A 11B 3QMAS experiment was conducted to obtain information on the spectral components of each 11B site. The obtained 3QMAS spectrum after shearing transformation [47] is shown in Fig. 4. For crystalline samples, the projection of the 3QMAS spectrum onto the indirect (F1) axis becomes a high-resolution spectrum, because inhomogeneous broadening caused by second-order quadrupole coupling is removed in this dimension. The F1 projection for 1 gave a resolved spectrum. The peaks at F1 ¼ 14.9 and 26.1 ppm are the spinning sidebands from a resonance at F1 ¼5.6 ppm. Note that
18
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
νr = 10 kHz corresponds to 20.6 ppm on the F1 axis, because of scaling by a factor of 9/34 in 3QMAS of I ¼3/2 nuclei [6]. Two distinct 11B sites are therefore present. 11 B NMR spectra for each 11B site can be retrieved by slicing the 11 B 3QMAS spectrum along the F2 axis at the resolved peak in the F1 axis. The two sliced spectra for 1 are shown on the right-hand
B (a)
O
B3circ
B3apex B4
(b)
B4 Fig. 3. Structure for one quarter of the hexadecaborate ring shown by (a) stick-andball model and (b) schematic representation. The green and gray circles show B and O atoms, respectively. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
side in Fig. 4. One more 11B component, which was observed in the 11 B MAS NMR spectrum but not detected in the 11B 3QMAS spectrum, is considered to be caused by its very small or very large quadrupole coupling. Spectral simulation was performed such that (i) the 11B MAS spectrum was fabricated from the sum of three 11B components with relative intensities of Bapex : Bcirc 3 : B4 = 1: 1: 2, 3 11 and (ii) two of the B components reproduce the slices of the 11B 3QMAS spectrum. The results of the spectral simulation, considering the secondorder quadrupole and isotropic shift interactions, are shown in Fig. 2(b) and the right-hand side of Fig. 4. The parameters of the quadrupole ( CQ , η) and isotropic shift (δ) interactions obtained by simulation are summarized in Table 2. For paramagnetic compounds, the isotropic component δ is the sum of the chemical shift ( δics) and the Fermi contact shift ( δFC ) due to the hyperfine coupling. However, δFC of 1 is expected to be small, because the spin densities of the unpaired electron spin at the 11B sites are very low [36] (vide infra). The NMR parameters were also obtained by DFT calculations, where δics is calculated as an isotropic value (Table 2). The analysis of the line broadening of the 11B NMR spectrum for the paramagnetic compound 1 is not straightforward. In the simulation, the broadening of each spectral component was adjusted simply by the effective spin–spin relaxation time ( T2⁎), and , Bcirc the values used for 11B of Bapex 3 , and B4 were 3.0 70.5, 3 1.0 70.2, and 0.5 70.04 ms, respectively. These values can be estimated, because the relative spectral intensity is also affected by T2⁎. The experimental value of the 11B spin–lattice relaxation time (T1) of 1 was 14 ms. The three 11B components were assigned as follows. (i) The components with large CQ values with relative spectral intensities of 1 and small CQ values with intensities of 2 are 11B of the BO3 and
Simulated component of the MAS spectrum
Observed -20
*
-10
F1 (ppm)
0
B3circ
10 20
*
30
B3apex
20
40 40
30
20 10 0 F2 (ppm)
10
0
υ / ppm
-10
20
10
0
υ / ppm
-10
-10 -20
Fig. 4. 11B 3QMAS NMR spectra of 1 at B0 ¼ 9.4 T and νr = 10 kHz . The asterisks in the map show the spinning sidebands. On the right-hand side, the slice spectra of 3QMAS at F1 ¼ 5.6 and 30.3 ppm are shown along with the theoretical spectra.
Table 2 NMR parameters of
11
B in {V12B32} obtained by spectral simulation and relativistic DFT calculation. η
δ/ppm
2.7 7 0.2
0.2 7 0.1
197 2
1.65 1.3 7 0.2
0.29 0.8 7 0.2
137 2
1.41 0.5 7 0.5 0.32
0.72 0.5 7 0.5 0.78
Site
Method
CQ /MHz
Bapex 3
By spectra By DFT By spectra By DFT By spectra By DFT
Bcirc 3 B4
δics/ppm
19 11 167 2 7
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
19
(a) Na(2)
Na(1)
Na(3)
Na(1) Na(2) Na(3)
Na(4)
(b)
Na*
50
0 υ / ppm (i)
Na(4) Na*
-50
40
20
0 -20 -40 υ / ppm (ii)
Fig. 5. 23Na MAS NMR spectra of 1 at (i) 9.4 and (ii) 21.6 T. (a) and (b) show the observed and simulated spectra, respectively. The red, blue, green, orange and black dashedlines in (b) show the spectral components by Na(1), Na(2), Na(3), Na(4) and Nan, respectively. The νr value was 16 kHz for both spectra. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
BO4 units, respectively. (ii) For the two types of BO3 unit, the sites and Bcirc with small and large η values correspond to Bapex 3 , re3 spectively. According to the previous studies for diamagnetic compounds [48,49], typical values for the 11B chemical shift are ∼20 ppm for BO3 and ∼0 ppm for BO4 units. Thus the present δics values for Bcirc and B4 are small and large, respectively, compared 3 to the literature values. Because the contribution of Fermi contact is not included in δics, these unusual δics values are considered to be due to the electronic structure of 1 adopting the open shell system and undergoing the antiferromagnetic coupling. The δ and δics values agreed well, except for B4. The disagreement in the B4 site may be caused by (I) the symmetry-imposed structure of {V12B32}, (II) other molecules (H2O and {V12B32}) surrounding the target {V12B32} molecule that were discarded in the DFT calculations, and (III) the Fermi contact shift. Although the η value for B4 could not be specified from the spectral simulation because of the small CQ value, the values of the other quadrupole parameters obtained by spectral simulation agreed with those obtained from DFT calculations, except in the . This disagreement can be caused by the reacase of CQ for Bapex 3 sons (I) and (II) above. The CQ value for Bcirc 3 seems somewhat small as a value for the BO3 unit. In the point-charge approximation (PCA), the component of the EFG tensor, eqαβ (α or β = x, y, z ), is expressed in SI units as [50,4]
eqαβ =
∑ j
qj
⎛ 3α β ⎞ ⎜ j j − δ ⎟, αjβj⎟ 2 rj ⎠
4π ϵ 0r j3 ⎜⎝
where the jth point-charge qj is at position
r 2j
=
x 2j
+
y2j
+
z 2j .
δαjβ and j
(1) (xj , yj , zj ) with
ϵ0 are the Kronecker delta and the free
space permittivity, respectively. By diagonalizing the EFG tensor of Eq. (1), the principal values are given. Considering the BO3 or BO4 unit and setting the charge for O2 as −2e , the eq33 values for Bapex , 3 21 21 Bcirc 3 , and B4 were calculated as 3.2 10 , 3.6 10 , and 20 2 circ 8.6 10 V m , respectively. The order eq33(B3 ) > eq33(Bapex ) 3
apex obtained by PCA is different from CQ (Bcirc ) by DFT cal3 ) < CQ (B3 culation and spectral simulation. This indicates that the small CQ (Bcirc 3 ) value is not simply caused by the local symmetry but the
charge distribution of 1. The sliced spectrum of 11B 3QMAS NMR at F1 ¼5.6 ppm was peak narrower than the simulated one. This is because the Bcirc 3 does not lie exactly along the F2 axis but is slightly inclined, because of the δ value distribution. In the MAS spectrum, this effect is taken into account by T2⁎. The poor signal-to-noise (SN) ratio of the observed sliced spectrum at F1 ¼ 30.3 ppm is the result of the large second-order quadrupole interaction for Bapex 3 ( CQ = 2.7 MHz ), causing spectral broadening and low conversion efficiency between single and triple quantum coherences. MQMAS spectra can also be analyzed by centers of gravity of the sliced spectra ( F2′ , F1′). If PQ = CQ 1 + η2/3 is defined as a second-order quadrupole effect, the values of δ (in units of parts per million) and PQ (in unit of hertz) can be estimated for the 3QMAS of I ¼3/2 nuclei as [6,51,52]
δ=
1 (17F1′ + 10F2′), 27
(2)
PQ =
ν 680 (F1′ − F2′) 03 , 27 10
where
ν0 is the resonance frequency. These equations give (δ, PQ )
(3)
and Bcirc as (25 ppm, 2.5 MHz) and (6 ppm, values for Bapex 3 3 0.9 MHz), respectively. There are some differences between the NMR parameters obtained by the analysis of the center of gravity and those by spectral simulation. This is due to the 11B 3QMAS spectrum that has the Bapex signal with low SN ratio and the 3 slightly inclined peak of Bcirc 3 . The 11B component that disappeared in the 3QMAS spectrum corresponds to B4. This is reasonable because both the spectral simulation and DFT calculation gave small CQ values, for which excitation to triple quantum coherence occurs inefficiently. Although the spectral lineshape of the 11B MAS NMR in Fig. 2 can be generated from CQ (for B4) up to 1.0 MHz, the value is considered to be very small. This small value is also expected from the BO4 structure, because the EFG of the nucleus at the center of the regular tetrahedral symmetry becomes zero by PCA. A slight distortion of BO4 from this symmetry causes the small CQ value in 1.
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T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
Table 3 23 Na NMR parameters of lativistic DFT calculation.
-40 (a)
QIS
F1 (ppm)
-20
CS
0
Na(1) Na(2)
20 Na(3) 40 40
F1 (ppm)
-10
20
0 -20 F2 (ppm)
-40
(b) Na(1)
0
Na(2)
10
Na(3) 20
CS 20
QIS 0 10 F2 (ppm)
-10
Fig. 6. 23Na 3QMAS NMR spectra of 1 at (a) 9.4 and (b) 21.6 T. The two solid lines indicated in the map show the axes of chemical shift (CS) and quadrupole-induced shift (QIS). The νr value was 16 kHz for both spectra.
For paramagnetic solids, in addition to the isotropic Fermi contact shift, the anisotropic interaction due to nuclear-electron dipole couplings ( /P ) can contribute to the spectra. The effect of /P on the 11B MAS spectra was examined in the Supporting Information (Figs. S1–S4). The spectral lineshape changed at slower MAS and larger anisotropy of /P . However, even at νr = 10 kHz , with only a slight change was found for the 11B MAS spectra of Bcirc 3 the anisotropy estimated for this site. Therefore, at least the contribution from the /P term in the spectral simulation in Fig. 2 (b) can be safely neglected. Experimentally, very intense spinning sidebands, which are a feature of the strong /P interaction, were not observed. 3.2. Structure of encapsulated Na ions by
23
Na NMR
Fig. 5(a-i) and (a-ii) show the 23Na MAS NMR spectra of 1 at 9.4 and 21.6 T, respectively. The broadened spectrum at 9.4 T
23
Na in {V12B32} obtained by spectral simulation and re-
Site
CQ /MHz
η
δ/ppm
〈By Spectra〉 Na(1) Na(2) Na(3) Na(4)
1.8 7 0.4 0.6 7 0.6 0.9 7 0.9 0.5 7 0.5
0.5 7 0.5 0.5 7 0.5 0.5 7 0.5 0.5 7 0.5
574 172 15 7 4 673
〈By DFT〉 Na
3.80
0.2
δics/ppm
26
narrowed at 21.6 T, as a result of the increase in the isotropic chemical shift (in hertz) and the decrease in the second-order quadrupole coupling when the high-field magnet is used (the chemical shift dispersion is not so large for this sample, as shown below). These spectra imply that there are at least two Na sites in 1. In order to improve the resolution, 23Na 3QMAS NMR spectra were obtained. The 3QMAS spectra obtained at 9.4 and 21.6 T are shown in Fig. 6(a) and (b), respectively. Clearly, three distinct 23Na sites are present in 1 (Na(1) to Na(3), from lower to higher frequency). For amorphous compounds, two lines, called the chemical shift (CS) axis and the quadrupole-induced shift (QIS) axis, are drawn in the MQMAS spectra [51,52]. The contours of the peaks in the 23Na 3QMAS spectra of Fig. 6 tend to lie along the CS axis, indicating a distribution of the chemical shift. The 23Na 3QMAS spectra can also be analyzed using Eqs. (2) and (3). With the maximum peak position of the 23Na 3QMAS spectra ( F2′ , F1′), the values of (δ, PQ ) for Na(1), Na(2), and Na(3) were estimated as ( 1 ppm, 1.6 MHz), (5 ppm, 0.8 MHz), and (18 ppm, 0.8 MHz), respectively, from the 23 Na 3QMAS at 9.4 T, and ( 7 ppm, 1.7 MHz), (0 ppm, 0.8 MHz), and (13 ppm, 0.8 MHz), respectively, at 21.6 T. The three 23Na sites were used to simulate the 23Na MAS spectra. The observed spectra, however, could not be reproduced by the superposition of these three sites alone. For example, a sharp peak at 12 ppm and a broad component extending across 20 to 40 ppm in Fig. 5(a-ii) are not generated by Na(1)–Na(3). The 23Na sites corresponding to these peaks are required to have very large or very small CQ values, because they were not observed in the 23Na 3QMAS spectra. By simulating the spectra at two magnetic fields, two separate 23Na sites (Na(4) and Nan) with very small CQ value were needed. The simulation results are shown in Fig. 5(b-i) and (b-ii). The NMR parameters for the sites Na(1)–Na (4) obtained by the simulation of the MAS spectra are summarized in Table 3. The line width of each spectral component was again adjusted by T2⁎, and the values were 0.3 7 0.1 ms for Na(1)–Na (3) and 0.55 70.1 ms for Na(4). The experimental 23Na T1 value of 1 was 2.7 ms. Setting the spectral intensity for Na(1) at 1.0, the relative intensities for Na(2), Na(3), and Na(4) were 0.19 70.11, 0.327 0.04, and 0.09 70.05, respectively. It is noted that because the low-frequency peak is very broad, the peak for the Na* site was produced by a Gaussian distribution. The peak center and standard deviation for the Gaussian were 29 73 and 6 7 1 ppm, respectively. The effect of the hyperfine interaction on the 23Na spectra was neglected as in the case of the 11B spectra. The isotropic component is not expected, because the electron spin density is almost localized on the V sites, and there are four bonds between the V and Na atoms. Furthermore, for the anisotropic component, the dipole interaction of 23Na–VIV is smaller than that of 11B–VIV because of the longer internuclear distance and small gyromagnetic ratio. From the simulation analysis for the paramagnetic effect (Figs. S5–S7), it is found that we can ignore the paramagnetic
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
contribution to the 23Na spectra of 1. Because of the fast spin relaxation, each spectral component was broadened and the η value could not be estimated. Considering that 1 + η2/3 can vary from 1.00 to 1.15, the quadrupole parameters obtained by spectral simulation are consistent with the PQ values obtained from the 23Na 3QMAS spectra. Although CQ for Na(4) was estimated as 0.5 7 0.5 MHz from the spectral simulation in Fig. 5, the value would be very small because the signal was not observed in the 23Na 3QMAS spectra. The CQ range for Na(2) is similar to that for Na(4) in Table 3. Thus, the Na (2) component, which exhibits the 23Na 3QMAS peak, is expected to have relatively large CQ value in the range. According to literature, the 23Na chemical shifts at room temperature have been reported as 5.3 to 8.8 ppm, 1.4 to 18.3 ppm [53], and 1.5 to 18.0 ppm, 1.2 to 14.4 ppm [54] for Na ions at cation sites within zeolites, and 20.5–2.4 ppm [55] for those within the zeolite-like Ge-framework. Thus, the estimated δ values for Na(1)–Na(4), collectively extending over 19 to 9 ppm, seem reasonable. Single-crystal X-ray data at room temperature [26] show that the four Na ions incorporated into the ring-shaped framework are located at the corners of a slightly distorted rectangular-parallelepiped with edge lengths of 267–273 and 285–287 pm. The multiple Na sites observed in the 23Na NMR spectra are therefore not so surprising. The Nan site may be due to the impurity incorporated in 1, because the δ value extends centered at 2973 ppm. A DFT calculation provided only a set of NMR parameters (Table 3), because the four Na ions are crystallographically equivalent in the simplified model considered in the calculations with D2d symmetry. A suitable method for examining the differences in the chemical shifts among the sites by DFT calculations is to use the X-ray structure or to perform geometry optimization for the Na ions. Unfortunately, the SCF calculations could not be converged without imposing symmetry. We therefore displaced the Na ions manually in a structure having an overall D2 symmetry. The calculation results for the Na-position dependence of the δics value of 23Na NMR are shown in Fig. 7. The coordinates are defined such that the four Na ions are located at ( x′, y′ , z′), ( x′, − y′ , − z′), ( −x′, y′ , − z′), and ( −x′, − y′ , z′). The values of Δx, Δy , and Δz are the displacements from the Na position in the original D2d structure. A negative displacement means that the Na ions approach the center of the cavity. At each Δz value, the δics values were calculated with the Δx and Δy values changing from 40 to 40 pm in steps of 20 pm. Basically, the maps in Fig. 7 are the upslope toward the lower left, and the gradient increases with decreasing Δz . The δics value at ( Δx, Δy , Δz )¼( 20 pm, 40 pm, 20 pm) was 4 ppm, which differs from the value at (0 pm, 0 pm, 0 pm) by 28 ppm. Therefore, the large difference of the δ values between the Na(1)–Na(4) sites can be understood. Because the simplified molecular structure was used in the DFT calculation, the absolute shift values obtained from the spectra and the DFT calculations differ, and large displacement of the Na position was required for explaining the observed 23Na shift. The relative spectral intensities (Fig. 5) indicate that the four Na ions occupy distinct sites with different populations. A similar phenomenon has been reported for the Na ions within the NaY zeolite [53]; three 23Na sites with different population were observed by NMR, contrary to a result from the molecular simulation predicting that the Na ions would be at a single site. The multiple sites were caused by a potential surface of the Na ion with multiple local minima. If the relative intensities of the 23Na peak of 1 are related to the potential surface in the cavity, the depth of the local minimum is in the order of Na(1) > Na(3) > Na(2) > Na(4). Thr bond energy of 1 was examined by the DFT calculation as a function of the displacement of the Na ion in the cavity (Fig. S8). Unlike the δics map in Fig. 7, the upslope of the contour toward the
21
40 (a) 20 Δy / pm 0 -20 -40 -40
-20
0 20 Δx / pm
40 δics / ppm 5 0
40 (b) 20
-5 -10
Δy / pm 0
-15 -20
-20
-25 -40 -40
-20
0 20 x / pm Δ
40
-20
0 20 Δx / pm
40
-30
40 (c) 20 Δy / pm 0 -20 -40 -40
Fig. 7. Contour maps for δics of 23Na NMR of {V12B32} obtained by relativistic DFT calculation and plotted as a function of Δx and Δy . (a), (b) and (c) show the plots at Δz = 0 , 10 and 20 pm, respectively. See text for the meaning of Δx, Δy and Δz .
lower left of the map was not simple for the bond energy, which may be due to the multiple local minima of the potential surface. Neither the accurate positions of the Na ions nor the type of disorder could be determined in the present analysis. The CQ values obtained by spectral simulation are smaller than those obtained from DFT calculations (Table 3). This can be ascribed to a slight change in the local symmetry of the Na sites. A partial averaging of the EFG tensor caused by fluctuation of the Na ions in the cavity may also reduce the CQ value. 3.3. Electron spin structure Seven d1 electrons are included in the [V7IVV5VB32O84]19 − anion.
22
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
(a)
(b)
cancelation of the up- and down-spins in the units, one up-spin is the total density for {V12B32}. The occupancy by VIV species is reduced to 7/12 for each V ion on average. It is noted that although the electronic structure can be altered by the position of the Na ions, no drastic position-dependence was obtained for the spin density distribution (Fig. S9). Because the spin density exhibits narrow spread on each V site, the Fermi contact interactions in the 11 B and 23Na NMR spectra are expected to be reduced considerably. Although we attempted to record 51V MAS NMR spectra of 1, no signal was observed. This result is consistent with the delocalized spin structure obtained from the DFT calculation, because the relaxation time of 51V is expected to be considerably short owing to the electron spins being distributed on all the V sites. If the electron spin is localized on a 51V site, the 51V NMR signals would be observed for other 51V sites [23], if the structural disorder of the framework is static. An X-band ESR signal at 7.2 K for the crystalline form of 1 was a singlet-like broadened spectrum without hyperfine structures (g ¼2.0 with peak-to-peak halfwidth, ΔHpp , of 47 mT) (Fig. S10). When VIV is delocalized over the 12 V sites, the spectrum consists of 85 lines caused by 2In þ1(I ¼7/2, n ¼12). Considering signal overlaps due to anisotropic interactions, the singlet-like broadened spectrum due mainly to intense peaks arising from Ieff = ± 3/2 and 71/2 is expected. Indeed, such an ESR spectrum ( ΔHpp ∼ 40 mT ) has been reported for a typical spin-frustration compound of K11H[(VO )3(SbW9O33)2]·27H2O [56], where effectively one d1 electron is delocalized over a VIV 3 ring, whereas the two other electrons are antiferromagnetically coupled. If the d1 electron is localized on a site, a narrower spectrum with eight lines will appear. Therefore, the above delocalized spin structure of 1 is also supported by the ESR spectrum.
4. Conclusion Fig. 8. Spin density distribution of {V12B32} obtained by relativistic DFT calculation. (a) and (b) show the top- and side-view, respectively. The distributions for the upand down-spins are indicated by blue and red, respectively. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Only one uncoupled electron is effective at room temperature, because of strong antiferromagnetic couplings, therefore the difference between the up- and down-spins was set at one in the DFT calculation. Here, we consider two types of molecular and electron spin structures [26]. One has structural disorder in the {V12B32} framework, where three sets of antiferromagnetic couplings occur as a result of the disorder of the V atoms (or the OVO4 pyramids), leaving one electron spin localized on a V IV site. The other is an average structure with electron spins delocalized over the ring. For the DFT calculation of the former structure, the symmetry of {V12B32} needs to be released, because three V–V pairs with short interatomic lengths are required for the framework structure. The SCF calculations for such structures, however, have never converged, as in the case for 23Na NMR. We therefore calculated the spin structure for the original D2d structure again, which is the average structure. The spin density distribution of the d1 electrons in {V12B32} obtained from the DFT calculation is shown in Fig. 8. Because of the symmetry, the electron spins were delocalized over the 12 V ions. A spin density unit consists of a down-spin with two up-spins on both sides, caused by antiferromagnetic interactions. This corresponds to a molecular structure with V–V interatomic distances of 289.4 pm for the V ions in the V–V–V unit, and 303.6 pm for those between the units. Because of partial
In conclusion, we studied the 11B and 23Na MAS and 3QMAS solid-state NMR spectra at 9.4 and 21.6 T for the mixed-valence paramagnetic polyoxovanadate(IV, V) of 1. The NMR parameters were estimated using spectral analysis and relativistic DFT calculations. The four Na ions incorporated into the ring-shaped framework occupied the four sites in the cavity, with different populations. The seven d1 electrons from VIV species were distributed over the 12 V ions, resulting in an average VIV occupancy of 7/12 for each of them. Future work will include (i) variable-temperature 11 B static NMR to observe the spectral change through the magnetic interaction and (ii) variable-temperature 23Na NMR and molecular dynamics simulation to investigate the motion of the Na ions in the cavity.
Acknowledgment This work was supported by the IMS molecule and material synthesis platform as a program of “Nanotechnology Platform” of MEXT, Japan. The financial support by JSPS Grant-in-Aid for Young Scientists (B) No. 24750026 is gratefully acknowledged.
Appendix A. Supplementary data Supplementary data associated with this paper can be found in the online version at http://dx.doi.org/10.1016/j.ssnmr.2016.03.004.
T. Iijima et al. / Solid State Nuclear Magnetic Resonance 76-77 (2016) 15–23
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